# Diagram algebras and integrable lattice models

**Project level: **PhD, Masters, Honours

Diagram algebras offer an intriguing mathematical environment where computations are performed by diagrammatic manipulations. Applications include knot theory and lattice models in statistical mechanics. Important examples of diagram algebras are the Temperley-Lieb algebras which can be used to describe lattice loop models of a large class of two-dimensional physical systems with nonlocal degrees of freedom in terms of extended polymers or connectivities. This project seeks to develop the representation theory of some of these diagram algebras and to apply the results to the corresponding integrable lattice loop models.